Secondary Resonance Research Articles

Biodynamic response of seated human body to roll vibration: Effect of armrest support

Human beings are exposed to whole-body vibration during daily life, which may cause discomfort or even sickness. Rotational vibration especially the roll vibration produces conspicuous discomfort. To promote the understanding of biodynamic characteristics of human body under roll vibration experimental research is carried out with eight subjects exposed to three levels of excitations. Different support conditions: rigid seat with and without armrests are applied and compared to investigate whether the armrest supports restrain or promote the response of human body to roll excitation. Apparent inertia is defined to represent the biodynamic characteristics of human body. A principal resonance at about 1 Hz and a secondary resonance at 2.5 Hz are detected in the roll apparent inertia. Armrest has little influence on the primary resonance frequency but decrease the first peak of apparent inertia, i.e., benefit the ride comfort. It is necessary that the height of armrests fits the stature of occupants so as to provide “effective” support and restrain occupants’ response. A lumped parameter model of seated human considering the support condition is proposed. The modal properties of human body are obtained.

Investigating the resonance response of a system of two ultrasound-driven lipid encapsulated microbubbles

Ultrasound-stimulated microbubbles are clinical imaging agents and being developed for therapeutic applications. Here, we aim to understand the behaviour of two individual phospholipid-encapsulated microbubbles in close proximity to each other, typically the case given clinical doses. We developed a finite element model to study the radial resonance response of each microbubble within a two-microbubble system from 1–8 MHz with bubble diameters ranging from 2 to 4 μm, bubble center-to-center distances h = 8–24 μm, and peak-negative pressures of 30–45 kPa. For two identical microbubbles, our results show the frequency of maximum response (fMR) decreases (7%–10%) and the amplitude of maximum response (AMR) increases (9%–11%) as the microbubbles approach one another. For a two-bubble system of different microbubble sizes, the larger microbubble shows no change in fMR and a slight shift of AMR (2–3%). However, the smaller microbubble exhibits an increase in fMR (7–11%) and a significant decrease of AMR (38–52%). Furthermore, when in very close proximity (h = 8 μm), smaller bubbles exhibit a secondary resonance peak corresponding to the fMR of the larger bubble with amplitudes comparable to its primary resonance peak. Our work suggests that microbubble resonance behaviour is greatly affected by the presence of nearby bubbles, which has implications in imaging and therapy.

Synchronous Signal Transmission Method of Minimally Invasive Renal Failure Surgery Based on Nano Molecular Image Probe.

The synchronous signal transmission can promote the successful completion of minimally invasive renal failure surgery, so the synchronous signal transmission method of minimally invasive renal failure surgery based on nano molecular image probe is studied. The nanoprobe is constructed by loading different signal molecules, photosensitizers, acoustic sensitizers and thermosensitives through the method of double emulsion or film hydration; the near-infrared confocal endoscope molecular image diagnosis and treatment equipment is designed based on the nanoprobe, and the intraoperative highfrequency image is obtained through the diagnosis and treatment equipment; the high-frequency injection energy and signal synchronous transmission method is adopted, and the signal is added to the primary and secondary resonance circuit. In the coupling module, a higher frequency alternating signal is added into the resonant coupling voltage to modulate the signal into the transmission resonance system, which is transmitted from the energy transmission coupling coil to the secondary end, and the injected signal part of the coupling coil is demodulated at the other end to complete the transmission of the signal coupling transmission loop, so as to realize the high-frequency image energy and index data signal of minimally invasive renal failure surgery. The experimental results show that the designed nano molecular image probe has good stability, and the simulated signal transmission waveform is consistent with the transmission waveform of the principle analysis. Applying the proposed method to the minimally invasive surgery of renal failure, it is found that the success rate and image signal transmission efficiency of the minimally invasive surgery of patients 1-5 are higher than 99.5%, and the operation image transmission accuracy is high and the operation effect is excellent.

A Conformal Frequency Reconfigurable Antenna with Multiband and Wideband Characteristics.

A compact flexible multi-frequency antenna for smart portable and flexible devices is presented. The antenna consists of a coplanar waveguide-fed slotted circular patch connected to a rectangular secondary resonator (stub). A thin low-loss substrate is used for flexibility, and a rectangular stub in the feedline is deployed to attain wide operational bandwidth. A rectangular slot is etched in the middle of the circular patch, and a p-i-n diode is placed at its center. The frequency reconfigurability is achieved through switching the diode that distributes the current by changing the antenna’s electrical length. For the ON state, the antenna operates in the UWB region for −10 dB impedance bandwidth from 2.76 to 8.21 GHz. For the OFF state of the diode, the antenna operates at the ISM band (2.45/5.8 GHz), WLAN band (5.2 GHz), and lower X-band (8 GHz) with a minimum gain of 2.49 dBi and a maximum gain of 5.8 dBi at the 8 GHz band. Moreover, the antenna retains its performance in various bending conditions. The proposed antenna is suitable for modern miniaturized wireless electronic devices such as wearables, health monitoring sensors, mobile Internet devices, and laptops that operate at multiple frequency bands.

Parametric resonance of bi-directional axial loads shallow arch microresonators

In this work, we investigate analytically and experimentally parametric resonances of an in-plane clamped-guided shallow arch microresonator. The arch is connected to a T-shaped moveable mass, which is sandwiched between two electrodes to electrostatically activate the device and to offer bi-directional axial loads option. The device is tested under primary and secondary parametric resonances. In addition, an analytical model is presented taking into account the initial rise of the microbeam and the sliding motion at the guided side. The static and free vibration problems are solved using the Differential Quadrature Method, and the dynamic response is simulated using an assumed mode Galerkin approximation. The theoretical results of the static and dynamic behavior of the device are compared to experimental data showing good agreement. Moreover, we demonstrate the use of parametric excitation to significantly amplify the axial motion. It is found that the second parametric resonance, corresponding to the fundamental mode of the arched microbeam, has a higher amplitude than the principal parametric case, due to the initial curvature of the beam. Thus, the proposed device can be a promising candidate for variety of sensing applications.

Investigating the potential disease-modifying and neuroprotective efficacy of exercise therapy early in the disease course of multiple sclerosis: The Early Multiple Sclerosis Exercise Study (EMSES)

Background: Potential supplemental disease-modifying and neuroprotective treatment strategies are warranted in multiple sclerosis (MS). Exercise is a promising non-pharmacological approach, and an uninvestigated ‘window of opportunity’ exists early in the disease course. Objective: To investigate the effect of early exercise on relapse rate, global brain atrophy and secondary magnetic resonance imaging (MRI) outcomes. Methods: This randomized controlled trial (n = 84, disease duration <2 years) included 48 weeks of supervised aerobic exercise or control condition. Population-based control data (Danish MS Registry) was included (n = 850, disease duration <2 years). Relapse rates were obtained from medical records, and patients underwent structural and diffusion-kurtosis MRI at baseline, 24 and 48 weeks. Results: No between-group differences were observed for primary outcomes, relapse rate (incidence-rate-ratio exercise relative to control: (0.49 (0.15; 1.66), p = 0.25) and global brain atrophy rate (−0.04 (−0.48; 0.40)%, p = 0.87), or secondary measures of lesion load. Aerobic fitness increased in favour of the exercise group. Microstructural integrity was higher in four of eight a priori defined motor-related tracts and nuclei in the exercise group compared with the control (thalamus, corticospinal tract, globus pallidus, cingulate gyrus) at 48 weeks. Conclusion: Early supervised aerobic exercise did not reduce relapse rate or global brain atrophy, but does positively affect the microstructural integrity of important motor-related tracts and nuclei.

Bifurcation analysis and nonlinear dynamics of a capacitive energy harvester in the vicinity of the primary and secondary resonances

The objective of the present study is to examine the effect of nonlinearity on the efficiency enhancement of a capacitive energy harvester. The model consists of a cantilever microbeam underneath which there is an electret layer with a surface voltage, which is responsible for the driving energy. The packaged device is exposed to unwanted harmonic mechanical excitation. The microbeam undergoes mechanical vibration, and accordingly, the energy is harvested throughout the output electric circuit. The dynamic formulation accounts for nonlinear curvature, inertia, and nonlinear electrostatic force. The efficiency of the device in the vicinity of the primary and super-harmonic resonances is examined, and accordingly, the output power is evaluated. Bifurcation analysis is carried out on the dynamics of the system by detecting the bifurcations in the frequency domain and diagnosing their respective types. One of the challenging issues in the design and analysis of energy-harvesting devices is to broaden the bandwidth so that more frequencies are potentially accomodated within the amplification region. In this study, the effect of the nonlinearity on the bandwidth broadening, as well as efficiency improvement of the device, are examined. It is seen that as the base excitation amplitude increases, the vibration amplitude does also increase and accordingly the nonlinearity dominates. The super-harmonic resonance regions emerge and get bigger as the vibration amplitude increases, and pull-in gaps appear in the frequency response curves.

Nonlinear vibration and resonance analysis of a rectangular hyperelastic membrane resting on a Winkler–Pasternak elastic medium under hydrostatic pressure

In this paper, the nonlinear vibration and resonance analyses of a rectangular hyperelastic membrane embedded within a nonlinear Winkler–Pasternak elastic medium subjected to a uniformly distributed hydrostatic pressure are investigated. The material of the membrane is incompressible, homogeneous, isotropic, and hyperelastic. The constitutive law of neo-Hookean is utilized for modeling the system. The elastic foundation includes two Winkler and Pasternak linear terms and a Winkler term with cubic nonlinearity. Using the theory of thin hyperelastic membrane, Hamilton’s principle, and assuming the finite deformations, the governing equations are obtained. Then, the motion equation in the transverse direction is discretized by applying Galerkin’s method. The transverse nonlinear oscillations of the membrane are considered in two-modes. Then, utilizing the multiple scales method, the secondary resonance for the case of is analyzed. Also, to analyze the nonlinear vibration behavior, numerical methods including the fourth-order Runge–Kutta methods are utilized. In addition, in analyzing the nonlinear vibration responses of the rectangular hyperelastic membrane, the bifurcation diagram, quasi-period motion responses, and the phase portrait are examined. Finally, the influence of the geometrical characteristics and elastic foundation parameters on the resonance analysis of a rectangular hyperelastic membrane is investigated.

Nonlinear multimodal model for an annular tuned sloshing damper equipped with damping screens

Annular tuned sloshing dampers equipped with damping screens are studied experimentally and analytically. A nonlinear multimodal model is presented to simulate the coupled response among the lowest order sloshing modes in a tank equipped with damping screens, which leads to velocity-squared damping. Shake table tests are conducted on annular tanks with various inner radii, water depths, screen orientations, and base excitation amplitudes. The proposed model is evaluated by comparing the predicted and measured sloshing forces, energy dissipation per cycle, and wave heights. The predicted sloshing forces and energy dissipation per cycle are in good agreement with the measured results. The wave heights show larger discrepancies, including phase shifts; however, the peak amplitudes are captured with reasonable accuracy for the tests conducted. Secondary resonances lead to multiple peaks in the frequency response plots when higher order sloshing modes become excited through modal coupling. Plots created to indicate which secondary resonances are likely to occur for a given liquid depth ratio indicate that it may not be possible to avoid all secondary resonances. Radial damping screens can be strategically positioned within the tank to provide the desired level of damping to the fundamental sloshing modes, as well as a reasonable amount of damping to higher order modes that are susceptible to secondary resonance excitation. Since existing linearized models for annular tuned sloshing dampers equipped with damping screens do not capture the important nonlinear response characteristics of these devices, the proposed model fills an important research gap necessary to facilitate their effective design.

On Nonlinear Oscillations of a Time-Periodic Hamiltonian System at a 2:1:1 Resonance

We consider the motions of a near-autonomous Hamiltonian system $2\pi$-periodic in time, with two degrees of freedom, in a neighborhood of a trivial equilibrium. A multiple parametric resonance is assumed to occur for a certain set of system parameters in the autonomous case, for which the frequencies of small linear oscillations are equal to two and one, and the resonant point of the parameter space belongs to the region of sufficient stability conditions. Under certain restrictions on the structure of the Hamiltonian of perturbed motion, nonlinear oscillations of the system in the vicinity of the equilibrium are studied for parameter values from a small neighborhood of the resonant point. Analytical boundaries of parametric resonance regions are obtained, which arise in the presence of secondary resonances in the transformed linear system (the cases of zero frequency and equal frequencies). The general case, for which the parameter values do not belong to the parametric resonance regions and their small neighborhoods, and both cases of secondary resonances are considered. The question of the existence of resonant periodic motions of the system is solved, and their linear stability is studied. Two- and three-frequency conditionally periodic motions are described. As an application, nonlinear resonant oscillations of a dynamically symmetric satellite (rigid body) relative to the center of mass in the vicinity of its cylindrical precession in a weakly elliptical orbit are investigated.

Comparative characteristics of the vaginal and endometrial microbiome in patients with secondary infertility associated with a uterine scar niche after cesarean section

Aim. To compare the vaginal and endometrial microbiome in patients with cesarean scar niche (both in the presence of specific complaints of secondary infertility in combination with a niche with stagnant contents, and in the absence of such).&#x0D; Materials and methods. The prospective study included 67 female patients of reproductive age who had a uterine scar after caesarean section that met the inclusion criteria. Depending on the presence or absence of clinical complaints of secondary infertility, ultrasound and/or magnetic resonance imaging of the pelvic organs to visualize stagnant content in the projection of the niche, the patients were divided into two groups: group 1 (n=40) patients with secondary infertility in combination with stagnant contents in the projection of a niche (main group), group 2 (n=27) patients without clinical complaints, with a formed scar on the uterus, without signs of a niche (control group). All patients underwent a comparative study of the vaginal samples and the endometrial samples. The species and quantitative composition of the microbiome was analyzed using real-time polymerase chain reaction. Statistical research was carried out using the IBM SPSS Statistica v22 software (IBM Corp., USA).&#x0D; Results. Various microbiological communities were found in the analysis of samples of the vagina and endometrium in patients with stagnant content in the projection of the niche (group 1, main) and without it (group 2, control). Lactobacillus spp. was found most often in vaginal discharge samples (more than 50% of cases) both in group 1 and in group 2, however, their level was statistically significantly higher in group 2 (57.5 and 88.9%, respectively), p=0.005. When comparing endometrial samples from patients of groups 1 and 2, it was revealed that in group 1, in the presence of liquid content in the projection of a niche, opportunistic microorganisms were most often detected (more than 50% of cases): Enterobacteriaceae (65%) p0.0001, Streptococcus spp. (60%) p0.0001, Staphylococcus spp. (52.5%) p0.0001, and Gardnerella spp. (22.5%) p=0.0342 and there was a deficiency of Lactobacillus spp. (25%), on the contrary, in group 2, Lactobacillus spp. prevailed (66.7%) p=0.008. Comparative analysis of vaginal samples and endometrial samples of the niche projection in group 1 revealed the predominance (more than 50% of cases) of Lactobacillus spp. in the vagina (57.5%) p=0.003, on the contrary, in the uterine cavity there is a predominance of opportunistic microbiota, p0.001. Comparative analysis of vaginal samples and endometrial samples of the uterine cavity in group 2 revealed a statistically significant predominance of Lactobacillus spp. both in the vagina (88.9%) and in the uterine cavity (66.7%), p=0.0497. In patients with secondary infertility associated with the presence of stagnant content in the projection of the niche, compared with the control group, there was a higher alpha-diversity both in the samples of vaginal discharge (Shannon's index 2.0170.093 vs 1.0600.044; p=0.0120), and in endometrial samples (Shannon's index 3.4480.267 vs 1.0200.040, р=0.00008; Simpson's index 1.109 vs 0.003; p=0.00006). When analyzing beta-diversity, there were no statistically significant differences between groups.&#x0D; Conclusion. In the structure of the microbiome of the vagina and uterine cavity in women without scar defect on the uterus Lactobacillus spp. predominate. The presence of stagnant content in the projection of a niche is associated with an increase in the frequency and quantitative content of opportunistic microbiota of the uterine cavity, especially Enterobacteriaceae, Streptococcus spp., Staphylococcus spp., Gardnerella spp. Also, in patients with stagnant contents in the projection of the niche, a higher biodiversity was revealed both in the vaginal discharge samples and in the endometrial samples. These results highlight the importance of assessing the endometrial microbiome in women with cesarean section scar, especially those faced with the problem of secondary infertility.

A Study on Nonlinear Dynamic Response of the Large-Span Roof Structure with Suspended Substructure

Nowadays, it is common to see large public buildings, e.g., stadiums, with some equipment or substructure suspended from the center of the roof. These substructures will tend to be larger and heavier the more gear is needed, which may have negative impacts on the dynamic performance of the roof structures. In this paper, to explore the dynamic response of a large-span roof structure with a suspended substructure, a real structure model is simplified into a two-degrees-of-freedom system. The essential consideration of nonlinear vibration is elaborated in the equations of motions. Approximate analytical solutions for free and forced vibrations are derived using perturbation methods, while numerical analysis is carried out to validate the solutions. The ratio of linear to nonlinear amplitude is proposed to represent the nonlinear effect of the primary structure, and the nonlinear effect, varying with structural parameters of frequency ratio, mass ratio, excitation ratio, and external force to the primary structure, is investigated. It is shown that internal resonance occurs when the structural frequency ratio is close to 1:2 and that secondary resonance takes place due to certain external excitations; internal resonance and secondary resonance will magnify the amplitude of the primary structure during vibration. Finally, a case of a designed practical dome with a suspended substructure is studied to verify the outcomes from the above research. According to these findings, some design proposals for this type of structure are provided.

An All-Textile Dual-Band Antenna for BLE and LoRa Wireless Communications

In this paper, a dual-band conductive textile-based wearable antenna operating at LoRa-868 MHz and BLE-2.4 GHz is presented. The proposed antenna is intended for accurate geolocation, tracking and communication applications in the military, industrial and telemedicine industries. The low-profile patch antenna is suitable for integrating into clothing. It is composed of three textile layers: top and bottom silver-ink-printed polystyrene fabrics, and a neoprene substrate. To utilize the flexible and restorable properties of these textile materials, the proposed antenna is directly fed by a flexible cable using an aperture-coupled feeding technique. This method not only eliminates the use of the conventional, bulky, and metallic SMA connector but also introduces a secondary resonance at 2.4 GHz, enabling the dual-band property. Using a thin coaxial cable fixed on the aperture slot for proximity coupling, a compact antenna size of 150 mm2 is obtained that can easily be attached and detached on existing cloths. The proposed structure has been fabricated and measured in an anechoic chamber to verify the performance. Measured gain of 3.28 dBi and 3.25 dBi was realized for LoRa and BLE at an antenna size of 0.61 λg × 0.61 λg × 0.012 λg (where λg is guided wavelength at 868 MHz) with a front-to-back ratio (FBR) of greater than 10 dBi.

Steady-state response of an axially moving circular cylindrical panel with internal resonance

With the 3:1 internal resonance, the primary and secondary resonances of an axially moving thin circular cylindrical panel are investigated in the present work. The governing equation and the compatibility equation are established based on the Donnell's nonlinear shell theory and solved to obtain the nonlinear steady-state responses by combining the Galerkin method and the method of multiple scales. The analytical solutions are verified by numerical solutions based on the Runge-Kutta Method. The governing equation includes both the quadratic nonlinearity and the cubic nonlinearity, so the perturbation solutions need to consider three time scales. The quadratic nonlinearity causes the softening behavior of the system. Natural frequencies and the 3:1 internal resonance condition are obtained by the linear analysis. Under the primary resonance, the internal resonance causes the coupling of the first two modes to complicate the nonlinear dynamic response. The response for the second mode possesses an extra bulge or peak due to the internal resonance. The quadratic nonlinearity results in the zero frequency drift and the second-order harmonic. Under the secondary resonance, the exciting force only arouses the second mode. Results are shown to examine the effects of the internal resonance, the exciting force and viscous damping coefficients on the nonlinear dynamic response of an axially moving thin circular cylindrical panel.

Characterization and interaction of geometric and contact/impact nonlinearities in dynamical systems

In this work, we study how a contact/impact nonlinearity interacts with a geometric cubic nonlinearity in an oscillator system. Specific focus is shown to the effects on bifurcation behavior and secondary resonances (i.e., super- and sub-harmonic resonances). The effects of the individual nonlinearities are first explored for comparison, and then the influences of the combined nonlinearities, varying one parameter at a time, are analyzed and discussed. Nonlinear characterization is then performed on an arbitrary system configuration to study super- and sub-harmonic resonances and grazing contacts or bifurcations. Both the cubic and contact nonlinearities cause a drop in amplitude and shift up in frequency for the primary resonance, and they activate high-amplitude subharmonic resonance regions. The nonlinearities seem to never destructively interfere. The contact nonlinearity generally affects the system’s superharmonic resonance behavior more, particularly with regard to the occurrence of grazing contacts and the activation of many bifurcations in the system’s response. The subharmonic resonance behavior is more strongly affected by the cubic nonlinearity and is prone to multistable behavior. Perturbation theory proved useful for determining when the cubic nonlinearity would be dominant compared to the contact nonlinearity. The limiting behaviors of the contact stiffness and freeplay gap size indicate the cubic nonlinearity is dominant overall. It is demonstrated that the presence of contact may result in the activation of several bifurcations. In addition, it is proved that the system’s subharmonic resonance region is prone to multistable dynamical responses having distinct magnitudes.

Photochemical transformation of pyridinium ionic liquids in aqueous phase: Kinetics, products and mechanism

Pyridinium ionic liquids (Pyr+ ILs) with promising applications are likely to appear in large quantity in water environment and become emergent pollutants due to their high hydrophilicity and low biodegradability. Hence, we studied the indirect photochemical degradation of Pyr+ ILs, including their kinetics of reactions with transient oxidants (•OH, CO3•–, triplet stated sodium anthraquinone-2-sulfonate (3AQ2S*) and 1O2), modeling studies on contribution of the transient oxidants to their degradation and their half-lives, as well as mechanistic study and toxicity estimation of the ILs and their products. Half-lives of these Pyr+ ILs were estimated to be 5–600 days under different scenarios, indicating persistence of the Pyr+ ILs in natural waters. Moreover, major contributors for degradation of the ILs are triplet stated dissolved organic matter (3DOM*) and CO3•―. For reaction with •OH, products identified by secondary mass spectrometry (MS2) and hydrogen nuclear magnetic resonance (1H NMR) indicate that the reactions proceed via hydrogen-atom transfer at the initial stage, and further transformation of the alkyl radicals lead to products by dehydrogenation, hydroxylation, and further oxidation. Additionally, model study shows that 1-butyl-Pyr+ and 1-butyl-3-methyl-Pyr+ IL are toxic to the aquatic organisms, and their products possess even higher toxicity, indicating that the Pyr+ ILs in natural waters may pose threat to aquatic organisms. Potential eco-risk of Pyr+ ILs should be fully considered before large-scale industrial application.

Efficiency of mono-stable piezoelectric Duffing energy harvester in the secondary resonances by averaging method, Part 2: Super-harmonic resonance

In the paper, the potential of harvesting vibratory energy via a mono-stable Duffing energy harvester with base excitation in super-harmonic resonance is investigated. The averaging method is exploited to provide an approximate analytical solution for the system. The displacement and voltage responses are determined depending explicitly on the displacement amplitude and excitation frequency. The explicit approximate analytical expressions of the peak amplitude and corresponding base excitation frequency are also presented. Next, a detailed power flow analysis in super-harmonic resonance is made, then formulations for input mechanical power and energy, useful electrical power and energy, and efficiency are obtained, respectively. Numerical simulations are carried out to show qualitative comparisons between sup- and sub-harmonic cases and linear cases at corresponding base excitation frequencies. It is obtained that super- and sub-harmonic resonances are effective solutions to enlarge the performance of nonlinear piezoelectric energy harvester in wide-band excitation, especially compared to linear one that only works at a single frequency.

Influence of the gap size on the response of a single-degree-of-freedom vibro-impact system with two-sided constraints: Experimental tests and numerical modeling

The large displacements caused by strong earthquakes in base-isolated structures (buildings, bridges, strategic facilities, equipment, ⋯) can excessively deform or damage the isolation system or lead to pounding with surrounding moat walls or adjacent structures, if the available seismic gap is not sufficient. The acceleration spikes caused by the impact can damage the structure itself as well as sensitive equipment housed in it. A possible mitigation measure consists in the interposition of deformable shock absorbers (bumpers). In this paper, the influence of the gap amplitude on the experimental response of a single-degree-of-freedom oscillator, excited by a harmonic base acceleration and symmetrically constrained by two unilateral deformable and dissipative bumpers, is investigated. The parametric investigation considered both positive, null, and negative gaps. Particular attention is paid to the study of the effect, on the system response, of the transition from positive to small negative gaps and of excessive negative gaps. Secondary resonances in the low frequency range, associated with the occurrence of multiple impacts, were experimentally observed for small positive gaps. Finally, the experimental results were reproduced, in a sufficiently accurate manner, using a suitable numerical model, whose parameters were identified based on the experimental data.

Nonlinear free and forced vibration of carbon nanotubes conveying magnetic nanoflow and subjected to a longitudinal magnetic field using stress-driven nonlocal integral model

In this paper primary and secondary resonance of carbon nanotube conveying magnetic nanofluid and subjected to a longitudinal magnetic field resting on viscoelastic foundation with different boundary conditions is investigated. To investigate the small scale effects, stress driven nonlocal integral model has been used and to show the more correctness of stress driven nonlocal integral model response, in studying the behavior of carbon nanotube with different boundary conditions, its results are compared with strain gradient model. The governing partial differential equations are derived from the Bernoulli–Euler beam theory utilizing the von Kármán strain–displacement relations. Using the Galerkin method, the governing equations are reduced to a nonlinear ordinary differential equation. The nonlinear natural frequencies are obtained from the perturbation method and the divergence and flutter instability due to the increase in nanofluid velocity is investigated. Then the frequency response for primary, subharmonic and superharmonic resonance is obtained using the method of multiple scales.Finally, the effects of length small scale parameters, longitudinal magnetic field, magnetic nanofluid and boundary conditions on nonlinear free and forced vibration of carbon nanotube are investigated. As the most important results, as the intensity of the magnetic field increases, the critical flow velocity increases and divergence and flutter occur later. But the critical flow velocity decreases with increasing the intensity of the magnetic field for a carbon nanotube conveying magnetic nanofluid. In forced vibration, increasing the intensity of the magnetic field increases the amplitude of the response for all boundary conditions in primary and secondary resonance.

Amplifying the response of a driven resonator via nonlinear interaction with a secondary resonator

We study the dynamics of a resonantly driven nonlinear resonator (primary) that is nonlinearly coupled to a non-resonantly driven linear resonator (secondary) with a relatively short decay time. Due to its short relaxation time, the secondary resonator adiabatically tracks the primary resonator and modifies its response. Our model, which is motivated by experimental studies on the interaction between nano- and micro-resonators, is relatively simple and can be analyzed analytically and numerically to show that the driven response of the primary resonator can be enhanced significantly due to the interaction with the secondary resonator. Such an arrangement may pave the way for systematic control of driven responses and signal amplification in engineering applications involving nano- and micro-electro-mechanical-systems.